Question 955755
the laws of exponents state:


{{{x^a * x^b = x^(a+b)}}}


{{{(x^a)^b = x^(a*b)}}}


{{{(x^a*y^b)^c = x^(ac) * y^(bc)}}}


{{{x^(-a) = 1/x^a}}}


{{{x^a = 1/x^(-a)}}}


your equation states:


{{{(1*.01)^36 = 1E-72}}}


since (1 * .01) is the same as (.01), your equation becomes:


{{{(.01)^36 = 1E-72}}}


1E-72 is the same as 1 * 10^(-72)


that's what it means.


your equation becomes:


{{{(.01)^36 = 1 * 10^(-72)}}}


.01 is the same as 1/100 which is the same as 1/10^2 which is the same as 1 * 10^(-2).


your equation becomes:


{{{(1 * 10^(-2))^36 = 1 * 10^(-72)}}}


since {{{(1 * 10^(-2))^36}}} is equivalent to {{{1^36 * (10^(-2))^36}}}, your equation becomes:


{{{1^36 * (10^(-2))^36 = 1 * 10^(-72)}}}


since 1^36 is equal to 1, your equation becomes:


{{{1 * (10^(-2))^36 = 1 * 10^(-72)}}}


since {{{(10^(-2))^36}}} is equal to {{{10^(-2*36)}}}, your equation becomes:


{{{1 * 10^(-2*36) = 1 * 10^(-72)}}}


since {{{10^(-2*36)}}} is equal to {{{10^(-72)}}}, your equation becomes:


{{{1 * 10^(-72) = 1 * 10^(-72)}}}


the equation is true because the left side is equal to the right side.


you have proven that:


(1*.01)^36 = 1E-72